If you know the rate that carbon-14 decays at, and how much of the carbon in a shroud, iceman or piece of old wood or bone is radioactive, you can work out how long ago they stopped breathing or photosynthesising. We know that on average it takes an atom of carbon-14 a little over 8,000 years to decay to nitrogen (although you never know when an individual atom is going to decay — it's completely random). But the value that's used to calculate the age of an object isn't an absolute figure, it's a statistical term called half-life.We even know that in a gram of carbon, 14 carbon-14 atoms turn into nitrogen every minute. The half-life of a radioactive isotope is the amount of time it takes for half of the atoms in a sample to decay. That means that no matter how many carbon-14 atoms were present when something died, after 5,730 years only half of them are left — the rest have decayed to nitrogen.
Read more on calibration and accuracy of radiocarbon dating.
Radiocarbon dating can easily establish that humans have been on the earth for over twenty thousand years, at least twice as long as creationists are willing to allow.
By about 58,000 years (ten half-lives) after an organism has died, there's so little radioactive carbon left (less than 1/1000) that calculations of age are no longer accurate.
That's why radiocarbon dating is only reliable for samples up to 50,000 years old.
So the proportion of carbon-14 inside living things is the same as the proportion of carbon-14 in the atmosphere at that time.
But when we stop eating, or when plants stop photosynthesising, our carbon-14 levels no longer get topped up.Chemically, carbon-14 is no different from non-radioactive carbon atoms, so it ends up in all the usual carbon places — one trillionth of the carbon atoms in air, plants, animals and us are radioactive.All radioactive atoms eventually decay into something more stable, and carbon-14 decays into nitrogen.It's not that the radioactive carbon in air or food doesn't decay, it does.But something else is going on that keeps producing new carbon-14 — otherwise it would have all turned to nitrogen millions of years ago.The exact age of an unknown sample can never be known for sure, so short of discovering a time machine, 95 per cent accuracy is as good as it gets.